Compact Belief State Representation for Task Planning

Abstract

Task planning in a probabilistic belief space generates complex and robust execution policies in domains affected by state uncertainty. The performance of a task planner relies on the belief space representation of the world. However, such representation becomes easily intractable as the number of variables and execution time grow. To address this problem, we developed a novel belief space representation based on the Cartesian product and union operations over belief substates. These two operations and single variable assignment nodes form And-Or directed acyclic graph of Belief States (AOBSs). We show how to apply actions with probabilistic outcomes and how to measure the probability of conditions holding true over belief states. We evaluated AOBSs performance in simulated forward state space exploration. We compared the size of AOBSs with the size of Binary Decision Diagrams (BDDs) that were previously used to represent belief state. We show that AOBSs representation more compact than a full belief state and it scales better than BDDs for most of the cases.